1/2x+4x+7=0

Solution for 1/2x+4x+7=0 equation:

1/2x+4x+7=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x+7=0

We multiply all the terms by the denominator


4x*2x+7*2x+1=0

Wy multiply elements

8x^2+14x+1=0

a = 8; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·8·1
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{41}}{2*8}=\frac{-14-2\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{41}}{2*8}=\frac{-14+2\sqrt{41}}{16}
$